We explore three seemingly disparate but related avenues of inquiry: expanding what is known about the properties of the poles of the Ihara zeta function, determining what information about a graph is recoverable from its Ihara zeta function, and strengthening the ties between the Ihara zeta functions of graphs which are related to each other through common operations on graphs. Using the singular value decomposition of directed edge matrices, we give an alternate proof of the bounds on the poles of Ihara zeta functions. We then give an explicit formula for the inverse of directed edge matrices and use the inverse to demonstrate that the sum of the poles of an Ihara zeta function is zero. Next we discuss the information about a graph recoverable from its Ihara zeta function and prove that the girth of a graph as well as the number of cycles whose length is the girth can be read directly off of the reciprocal of the Ihara zeta function. We demonstrate that a graph's chromatic polynomial cannot in general be recovered from its Ihara zeta function and describe a method for constructing families of graphs which have the same chromatic polynomial but different Ihara zeta functions. We also show that a graph's Ihara zeta function cannot in general be recovered from its chromatic polynomial. Then we make the deletion of an edge from a graph less jarring (from the perspective of Ihara zeta functions) by viewing it as the limit as k goes to infinity of the operation of replacing the edge in the original graph we wish to delete with a walk of length k. We are able to prove that the limit of the Ihara zeta functions of the resulting graphs is in fact the Ihara zeta function of the original with the edge deleted. We also improve upon the bounds on the poles of the Ihara zeta function by considering digraphs whose adjacency matrices are directed edge matrices

This dissertation is an intervention into Critical Whiteness Studies, an ‘additional movement’ to Ethnic Studies and Critical Race Theory. It systematically analyzes key contradictions in working against racism from a white subject positions under post-Civil Rights Movement liberal color-blind white hegemony and "Black Power" counter-hegemony through a critical assessment of two major competing projects in theory and practice: white anti-racism [Part 1] and New Abolitionism [Part 2].

I argue that while white anti-racism is eminently practical, its efforts to hegemonically rearticulate white are overly optimistic, tend toward renaturalizing whiteness, and are problematically dependent on collaboration with people of color. I further argue that while New

Abolitionism has popularized and advanced an alternative approach to whiteness which understands whiteness as ‘nothing but oppressive and false’ and seeks to ‘abolish the white race’, its ultimately class-centered conceptualization of race and idealization of militant nonconformity has failed to realize effective practice.

Part 3 considers alternative identities to whiteness, argues for a stronger race-centered definition of whiteness as a secular coalition of previously antagonistic european peoples forged on global frontiers for the purposes of dispossessing, exploiting, and killing people of color, advances a framework for understanding processes of ‘becoming white’ without ‘necessary correspondence to class’, and proposes an alternative approach to ‘abolishing the white race’ focused on its internal ‘ethnic fissures’ called intersectional, anti-white, Irish Diasporic nationalism.